Cover13; -- Copyright -- Preface -- Motivation13; -- Feature of the Book13; -- Acknowledgements13; -- Contents -- Chapter 1. Discrete Theory, Relations and Functions -- 1.1 Introduction -- 1.2 Elementary Theory of Sets 13; -- 1.3 Set Rules and Sets Combinations -- 1.3.1 Rule of Equality13; -- 1.3.2 Study of Sets Combinations13; -- 1.3.3 Power Set -- 1.3.4 Multisets -- 1.3.5 Ordered Sets -- 1.3.6 Cartesian Products13; -- 1.4 Relations -- 1.4.1 Binary Relation -- 1.4.2 Equivalence Relation -- 1.4.3 Pictorial Representation of Relations -- 1.4.4 Composite Relation -- 1.4.5 Ordering Relation -- 1.5 Function -- 1.5.1 Classification of Functions13; -- 1.5.2 Composition of Functions -- 1.5.3 Inverse Functions -- 1.5.4 Recursively Defined Functions -- 1.6 Mathematical Induction and Piano's Axioms13; -- Chapter 2. Discrete Numeric Functions and Generating Functions -- 2.1 Introduction -- 2.2 Properties of Numeric Functions -- 2.2.1 Addition of numeric functions13; -- 2.2.2 Multiplication of Numeric Functions13; -- 2.2.3 Multiplication with a Scalar Factor to Numeric Function13; -- 2.2.4 Quotient of Numeric Functions -- 2.2.5 Modulus of Numeric Function13; -- 2.2.6. S1an and S1an13; -- 2.2.7 Accumulated Sum of Numeric Fuctions13; -- 2.2.8 Forward Difference & Backward Difference -- 2.2.9 Convolution of Numeric Functions -- 2.3 Asymptotic Behavior (Performance) of Numeric Functions13; -- 2.3.1 Big-Oh (O) Notation13; -- 2.3.2 Omega (937;) Notation 13; -- 2.3.3 Theta (952;) Notation13; -- 2.4 Generating Functions -- 2.5 Application of Generating Function to Solve Combinatorial Problems -- Chapter 3. Recurrence Relations with Constant Coefficients -- 3.1 Introduction -- 3.2 Recurrence Relation for Discrete Numeric Functions -- 3.3 Finding the Solution of LRRCC -- 3.3.1 Method of Finding Homogenous Solution -- 3.3.2 Method of Finding Particular Solution -- 3.4 Alternate Method (Finding Solution of LRRCC by Generating Function) -- 3.5 Common Recurrences from Algorithms -- 3.6 Method for Solving Recurrences -- 3.6.1 Iteration Method -- 3.6.2 Master Theorem -- 3.6.3 Substitution Method -- 3.7 Matrix Multiplication -- Chapter 4. Algebraic Structure -- 4.1 Introduction -- 4.2 Groups -- 4.3 Semi Subgroup -- 4.4 Complexes -- 4.5 Product Semigroups -- 4.6 Permutation Groups -- 4.7 Order of a Group -- 4.8 Subgroups -- 4.9 Cyclic Groups -- 4.10 Cosets -- 4.11 Group Mapping -- 4.12 Rings -- 4.13 Fields -- Chapter 5. Propositional Logic -- 5.1 Introduction to Logic -- 5.2 Symbolization of Statements -- 5.3 Equivalence of Formula -- 5.4 Propositional Logic -- 5.4.1 Well Formed Formula (wff)13; -- 5.4.2 Immediate Subformula -- 5.4.3 Subformula -- 5.4.4 Formation Tree of a Formula13; -- 5.4.5 Truth Table -- 5.5 Tautology -- 5.6 Theory of Inference -- 5.6.1 Validity by Truth Table -- 5.6.2 Natural Deduction Method -- 5.6.3 Analytical Tableaux Method (ATM) -- 5.7 Predicate Logic -- 5.7.1 Symbolization of Statements Using Predicate13; -- 5.7.2 Variables and Quantifiers -- 5.7.3 Free and Bound Variables13; -- 5.8 Inference Theory of Predicate Logic -- Chapter 6. Lattice Theory -- 6.1 Introduction -- 6.2 Partial Ordere.